One of the outstanding fundamental needs for ferroelectric thin films is developing a stable polar phase when the polarization has a component perpendicular to the film plane. Although such orientations are desired for many applications and can be obtained (e.g., by compressive epitaxial strain), the polarization change at the film boundaries creates a “depolarizing field” that should be neutralized for the polar phase to be stable. Two mechanisms appear to be available to reduce the depolarizing field energy: compensation by free charge at the boundaries or the formation of equilibrium stripe domains with oppositely oriented polarization. In both cases, the trade-off between bulk energy gain and surface energy cost leads to a suppression of the phase transition to the polar phase as films become thinner. These fundamental size effects may dramatically alter behavior in ultrathin films.